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Necessary and sufficient conditions for existence of blow‐up solutions for elliptic problems in Orlicz–Sobolev spaces
Author(s) -
Santos Carlos Alberto,
Zhou Jiazheng,
Abrantes Santos Jefferson
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600231
Subject(s) - mathematics , sobolev space , mathematical proof , bounded function , pure mathematics , class (philosophy) , domain (mathematical analysis) , nonlinear system , mathematical analysis , maximum principle , mathematical optimization , geometry , physics , quantum mechanics , artificial intelligence , computer science , optimal control
This paper is principally devoted to revisit the remarkable works of Keller and Osserman and generalize some previous results related to the those for the class of quasilinear elliptic problemdiv ϕ ( | ∇ u | ) ∇ u = a ( x ) f ( u )in Ω ,u ≥ 0in Ω ,u = ∞ on ∂ Ω ,where either Ω ⊂ R Nwith N ≥ 1 is a smooth bounded domain or Ω = R N . The function ϕ includes special cases appearing in mathematical models in nonlinear elasticity, plasticity, generalized Newtonian fluids, and in quantum physics. The proofs are based on comparison principle, variational methods and topological arguments on the Orlicz–Sobolev spaces.